Is there a way to define the midpoint between points in projective space?
2026-03-30 06:43:58.1774853038
Mipoint between points in projective space
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You can map any three points on a line to any three other using a projective transformation. So there exists a projective transformation which fixes the two points you have but maps your supposed midpoint anywhere at all. Therefore there can be no definition of a midpoint which is invariant under projective transformations.
If you fix one hyperplane as the set of points at infinity, then you can use that to define a midpoint: The midpoint of $AB$ would be the point $M$ satisfying $\operatorname{CR}(A,B;F,M)=-1$ where $F$ is the point at infinity on the line $AB$.